Magnetism and Matter Chapter-Wise Test 8

Correct answer Carries: 4.

Wrong Answer Carries: -1.

A material with \( \mu_r = 150 \) and \( H = 800 \, \text{A m}^{-1} \) has \( B \): (Take \( \mu_0 = 4\pi \times 10^{-7} \, \text{T m A}^{-1} \)).

\( B = \mu_0 \mu_r H \).

Given: \( \mu_r = 150 \), \( H = 800 \, \text{A m}^{-1} \), \( \mu_0 = 4\pi \times 10^{-7} \).

\( B = 4\pi \times 10^{-7} \times 150 \times 800 = 0.15072 \, \text{T} \approx 0.15 \, \text{T} \).

0.12 T
0.14 T
0.15 T
0.16 T
3

If a bar magnet is broken into two pieces, each piece retains both a north and a south pole. This observation supports the idea that:

Unlike electric charges, magnetic poles cannot be isolated. Breaking a magnet creates two smaller magnets, each with its own north and south pole, indicating that magnetic monopoles do not exist in nature, a key principle in magnetism.

Magnetic monopoles do not exist
Magnetic fields can be shielded completely
Magnetic poles can be separated
The magnet loses its magnetism upon breaking
1

A material placed in a magnetic field increases the field inside it slightly and moves toward stronger field regions. This behavior is characteristic of:

Paramagnetic materials have a small positive susceptibility (\( \chi > 0 \)), causing a slight enhancement of the magnetic field inside them due to the weak alignment of atomic magnetic moments with the external field. They are attracted to regions of stronger field strength.

Diamagnetic materials
Paramagnetic materials
Ferromagnetic materials
Superconductors
2

Which property of magnetic field lines distinguishes them from electric field lines in the context of a dipole?

Magnetic field lines form continuous closed loops because there are no magnetic monopoles; they emerge from the north pole and enter the south pole, looping back internally. In contrast, electric field lines of a dipole start at the positive charge and end at the negative charge, or extend to infinity if unterminated.

They form continuous closed loops
They originate and terminate on charges
They intersect at points of high field strength
They are always straight lines
1

A bar magnet with magnetic moment \( 1.8 \, \text{A m}^2 \) is placed at a distance of \( 0.5 \, \text{m} \) along its axis. What is the magnetic field \( B \) at that point? (Take \( \mu_0 = 4\pi \times 10^{-7} \, \text{T m A}^{-1} \)).

The magnetic field along the axis is \( B = \frac{\mu_0}{4\pi} \frac{2m}{r^3} \).

Given: \( m = 1.8 \, \text{A m}^2 \), \( r = 0.5 \, \text{m} \), \( \frac{\mu_0}{4\pi} = 10^{-7} \).

Substitute: \( B = 10^{-7} \times \frac{2 \times 1.8}{(0.5)^3} = 10^{-7} \times \frac{3.6}{0.125} = 2.88 \times 10^{-6} \, \text{T} \).

2.88 × 10⁻⁶ T
3.0 × 10⁻⁶ T
3.2 × 10⁻⁶ T
3.5 × 10⁻⁶ T
1

A material has \( B = 0.3 \, \text{T} \) and \( M = 1.5 \times 10^5 \, \text{A m}^{-1} \). What is \( H \)? (Take \( \mu_0 = 4\pi \times 10^{-7} \, \text{T m A}^{-1} \)).

\( B = \mu_0 (H + M) \), so \( H = \frac{B}{\mu_0} - M \).

Given: \( B = 0.3 \, \text{T} \), \( M = 1.5 \times 10^5 \, \text{A m}^{-1} \), \( \mu_0 = 4\pi \times 10^{-7} \).

\( \frac{B}{\mu_0} = \frac{0.3}{4\pi \times 10^{-7}} \approx 2.387 \times 10^5 \, \text{A m}^{-1} \).

\( H = 2.387 \times 10^5 - 1.5 \times 10^5 = 8.87 \times 10^4 \, \text{A m}^{-1} \approx 8.9 \times 10^4 \).

8.5 × 10⁴ A m⁻¹
8.9 × 10⁴ A m⁻¹
9.2 × 10⁴ A m⁻¹
9.5 × 10⁴ A m⁻¹
2

A material with \( \mu_r = 400 \) and \( H = 500 \, \text{A m}^{-1} \) has \( B \): (Take \( \mu_0 = 4\pi \times 10^{-7} \, \text{T m A}^{-1} \)).

\( B = \mu_0 \mu_r H \).

Given: \( \mu_r = 400 \), \( H = 500 \, \text{A m}^{-1} \), \( \mu_0 = 4\pi \times 10^{-7} \).

\( B = 4\pi \times 10^{-7} \times 400 \times 500 = 0.2512 \, \text{T} \approx 0.25 \, \text{T} \).

0.22 T
0.24 T
0.25 T
0.27 T
3

A bar magnet with \( m = 1.5 \, \text{A m}^2 \) produces a field at \( 0.5 \, \text{m} \) on its equatorial line. What is \( B \)? (Take \( \mu_0 = 4\pi \times 10^{-7} \, \text{T m A}^{-1} \)).

\( B = \frac{\mu_0}{4\pi} \frac{m}{r^3} \).

Given: \( m = 1.5 \, \text{A m}^2 \), \( r = 0.5 \, \text{m} \), \( \frac{\mu_0}{4\pi} = 10^{-7} \).

\( B = 10^{-7} \times \frac{1.5}{(0.5)^3} = 10^{-7} \times \frac{1.5}{0.125} = 1.2 \times 10^{-6} \, \text{T} \).

1.0 × 10⁻⁶ T
1.1 × 10⁻⁶ T
1.2 × 10⁻⁶ T
1.3 × 10⁻⁶ T
3

The reason magnetic field lines are denser near the poles of a magnet is:

The density of magnetic field lines indicates the field strength. Near the poles, the field is strongest because the lines converge or diverge there, reflecting the concentration of magnetic influence at these points.

The field is uniform
The poles are electrically charged
The field strength is greatest there
The magnet is weaker at the center
3

A material with \( B = 0.25 \, \text{T} \) and \( H = 1500 \, \text{A m}^{-1} \) has \( M \): (Take \( \mu_0 = 4\pi \times 10^{-7} \, \text{T m A}^{-1} \)).

\( B = \mu_0 (H + M) \), so \( M = \frac{B}{\mu_0} - H \).

Given: \( B = 0.25 \, \text{T} \), \( H = 1500 \, \text{A m}^{-1} \), \( \mu_0 = 4\pi \times 10^{-7} \).

\( \frac{B}{\mu_0} = \frac{0.25}{4\pi \times 10^{-7}} \approx 1.99 \times 10^5 \, \text{A m}^{-1} \).

\( M = 1.99 \times 10^5 - 1500 \approx 1.975 \times 10^5 \, \text{A m}^{-1} \).

1.8 × 10⁵ A m⁻¹
1.9 × 10⁵ A m⁻¹
1.95 × 10⁵ A m⁻¹
1.975 × 10⁵ A m⁻¹
4

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